8.1.1 Advanced Indexing

An array with ‘n’ dimensions can be indexed using ‘m’
indices. More generally, the set of index tuples determining the
result is formed by the Cartesian product of the index vectors (or
ranges or scalars).

For the ordinary and most common case, m == n, and each
index corresponds to its respective dimension. If m < n
and every index is less than the size of the array in the
i^{th} dimension, m(i) < n(i), then the index expression
is padded with trailing singleton dimensions ([ones (m-n, 1)]).
If m < n but one of the indices m(i) is outside the
size of the current array, then the last n-m+1 dimensions
are folded into a single dimension with an extent equal to the product
of extents of the original dimensions. This is easiest to understand
with an example.

One advanced use of indexing is to create arrays filled with a single
value. This can be done by using an index of ones on a scalar value.
The result is an object with the dimensions of the index expression
and every element equal to the original scalar. For example, the
following statements

a = 13;
a(ones (1, 4))

produce a vector whose four elements are all equal to 13.

Similarly, by indexing a scalar with two vectors of ones it is
possible to create a matrix. The following statements

a = 13;
a(ones (1, 2), ones (1, 3))

create a 2x3 matrix with all elements equal to 13.

The last example could also be written as

13(ones (2, 3))

It is more efficient to use indexing rather than the code construction
scalar * ones (N, M, …) because it avoids the unnecessary
multiplication operation. Moreover, multiplication may not be
defined for the object to be replicated whereas indexing an array is
always defined. The following code shows how to create a 2x3 cell
array from a base unit which is not itself a scalar.

{"Hello"}(ones (2, 3))

It should be, noted that ones (1, n) (a row vector of ones)
results in a range (with zero increment). A range is stored
internally as a starting value, increment, end value, and total number
of values; hence, it is more efficient for storage than a vector or
matrix of ones whenever the number of elements is greater than 4. In
particular, when ‘r’ is a row vector, the expressions

r(ones (1, n), :)

r(ones (n, 1), :)

will produce identical results, but the first one will be
significantly faster, at least for ‘r’ and ‘n’ large enough.
In the first case the index is held in compressed form as a range
which allows Octave to choose a more efficient algorithm to handle the
expression.

A general recommendation, for a user unaware of these subtleties, is
to use the function repmat for replicating smaller arrays into
bigger ones.

A second use of indexing is to speed up code. Indexing is a fast
operation and judicious use of it can reduce the requirement for
looping over individual array elements which is a slow operation.

Consider the following example which creates a 10-element row vector
a containing the values
a(i) = sqrt (i).

for i = 1:10
a(i) = sqrt (i);
endfor

It is quite inefficient to create a vector using a loop like this. In
this case, it would have been much more efficient to use the
expression

a = sqrt (1:10);

which avoids the loop entirely.

In cases where a loop cannot be avoided, or a number of values must be
combined to form a larger matrix, it is generally faster to set the
size of the matrix first (pre-allocate storage), and then insert
elements using indexing commands. For example, given a matrix
a,

because Octave does not have to repeatedly resize the intermediate
result.

: ind =sub2ind(dims, i, j)

: ind =sub2ind(dims, s1, s2, …, sN)

Convert subscripts to linear indices.

Assume the following 3-by-3 matrices. The left matrix contains the
subscript tuples for each matrix element. Those are converted to
linear indices shown in the right matrix. The matrices are linearly
indexed moving from one column to next, filling up all rows in each
column.

Assume the following 3-by-3 matrices. The left matrix contains
the linear indices ind for each matrix element. Those are
converted to subscript tuples shown in the right matrix. The
matrices are linearly indexed moving from one column to next,
filling up all rows in each column.

The following example shows how to convert the linear indices
2 and 8 in a 3-by-3 matrix into a subscripts.

ind = [2, 8];
[r, c] = ind2sub ([3, 3], ind)
⇒ r = 2 2
⇒ c = 1 3

If the number of subscripts exceeds the number of dimensions, the
exceeded dimensions are treated as 1. On the other hand,
if less subscripts than dimensions are provided, the exceeding
dimensions are merged. For clarity see the following examples:

If present, n specifies the maximum extent of the dimension to be
indexed. When possible the internal result is cached so that subsequent
indexing using ind will not perform the check again.

Implementation Note: Strings are first converted to double values before the
checks for valid indices are made. Unless a string contains the NULL
character "\0", it will always be a valid index.

: val =allow_noninteger_range_as_index()

: old_val =allow_noninteger_range_as_index(new_val)

: allow_noninteger_range_as_index(new_val, "local")

Query or set the internal variable that controls whether non-integer
ranges are allowed as indices.

This might be useful for MATLAB compatibility; however, it is still not
entirely compatible because MATLAB treats the range expression
differently in different contexts.

When called from inside a function with the "local" option, the
variable is changed locally for the function and any subroutines it calls.
The original variable value is restored when exiting the function.